sin π/12 -根号3cos π/12的值为：-根号2?为什么.

sin π/12 -根号3cos π/12的值为：-根号2?为什么.
sin π/12 -根号3cos π/12的值为：-根号2?为什么.

sin π/12 -根号3cos π/12的值为：-根号2?为什么.
原式=2(1/2sinπ/12-√3/2cosπ/12)
=2(sinπ/12*cosπ/3-cosπ/12*sinπ/3)
=2sin(π/12-π/3)
=2sin(-π/4)
=-2*√2/2=-√2
sin(α-β)=sinαcoβ-cosαsinβ
sin60°=sinπ/3

sinπ/12-√3cosπ/12=2[(1/2)sinπ/12-(√3/2)cosπ/12].
=2sin(π/12-π/6).
=2sin(-π/12)
=-2sinπ/12
=-2sin(π/4-π/6)
=-2[sinπ/4cosπ/6-cosπ/4sinπ/6).
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sinπ/12-√3cosπ/12=2[(1/2)sinπ/12-(√3/2)cosπ/12].
=2sin(π/12-π/6).
=2sin(-π/12)
=-2sinπ/12
=-2sin(π/4-π/6)
=-2[sinπ/4cosπ/6-cosπ/4sinπ/6).
=-2[√2/2*√3/2-√2/2*(1/2)]
=-2√2/4(√3-1)
=-(√2/2)(√3-1).
原题不可能=-√2.

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